We construct P(ϕ)1-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ essentially by sample path regularity. Associated with these processes we define a martingale which, under an appropriate scaling, allows to obtain a central limit theorem for additive functionals of these processes. We discuss a number of examples by choosing specific functionals related to particle-field operators.

中文翻译：

---

相对论和非相对论纳尔逊模型的泛函中心极限定理和 P(ϕ)1-过程

我们构建了由完整时间线索引的 P(φ)1-过程，分别从量子场论中相对论和非相对论纳尔逊模型的函数积分表示导出。这两种情况在样本路径规律性上有本质区别。与这些过程相关联，我们定义了一个鞅，在适当的缩放比例下，可以获得这些过程的加性泛函的中心极限定理。我们通过选择与粒子场算子相关​​的特定函数来讨论许多示例。